Take for instance a curved line.
You want to find the slope m of the curve at point (x,y).

There are a few procedures such as the tangential rule or the secant rule.

But simplictically, assume x is midway between 2 points x1 and x2, and y is midway between corrsponding points y1 and y2.
Then m = (y2-y1)/(x2-x1)
Or, m= Δy / Δx ( if y2-y1 and x2-x1 are not too great )

As Δx or Δy is made to become smaller and smaller to the limit of approaching 0(zero)
Then m=dx/dy